Heat grill. In medium bowl, combine ground beef and 1 teaspoon of the lemon-pepper seasoning; mix well. Shape mixture into 4 patties, 1/2 inch thick.
In medium bowl, combine mushrooms, remaining 1/2 teaspoon lemon-pepper seasoning and vinaigrette; toss to coat. Set aside.
When ready to grill, place patties on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 11 to 13 minutes or until patties are thoroughly cooked, turning once.
To toast rolls, place cut sides down on grill during last 1 to 2 minutes of cooking time. Place 1 slice of cheese on each patty; cook an additional minute or until cheese is melted.
Place patties on bottom halves of rolls. Top each with mushroom mixture and top half of roll.